Permutative universal realizability

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2021-01-01 DOI:10.1515/spma-2020-0123

R. Soto, Ana Julio, Jaime H. Alfaro

引用次数: 1

Abstract

Abstract A list of complex numbers Λ is said to be realizable, if it is the spectrum of a nonnegative matrix. In this paper we provide a new sufficient condition for a given list Λ to be universally realizable (UR), that is, realizable for each possible Jordan canonical form allowed by Λ. Furthermore, the resulting matrix (that is explicity provided) is permutative, meaning that each of its rows is a permutation of the first row. In particular, we show that a real Suleĭmanova spectrum, that is, a list of real numbers having exactly one positive element, is UR by a permutative matrix.

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置换的普遍可实现性

摘要复数∧的列表被认为是可实现的，如果它是非负矩阵的谱。在本文中，我们给出了一个新的充分条件，使给定的列表∧是普遍可实现的（UR），即对于∧所允许的每个可能的Jordan正则形式都是可实现的。此外，得到的矩阵（即显式矩阵）是置换的，这意味着它的每一行都是第一行的置换。特别地，我们证明了一个实的Suleĭmanova谱，即一个恰好有一个正元素的实数列表，是置换矩阵的UR。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.